Curved Factor Analysis with the Ellipsoid-Gaussian Distribution
Year: 2025
Type: article
Abstract: There is a need for new models that can capture dependence structures in multivariate data. While the multivariate Gaussian distribution is routinely used, it cannot characterize nonlinear relationships. Most nonlinear extensions are highly complex; for example involving the estimation of a nonlinear regression model in latent variables. In this article, we propose a relatively simple multivariate distribution called the Ellipsoid-Gaussian, which is derived from a Gaussian linear factor model with latent variables following a von Mises-Fisher distribution on the unit hyper-sphere. We show that the Ellipsoid-Gaussian distribution can flexibly model curved relationships among variables while maintaining lower-dimensional structures. Taking a Bayesian approach, we propose a hybrid posterior sampling method that combines gradient-based geodesic Monte Carlo with adaptive Metropolis. We establish key theoretical properties and demonstrate the practical utility of the Ellipsoid-Gaussian distribution through both simulated and real data applications. An accompanying R package is provided to facilitate implementation.
Source: Bayesian Analysis
DOI: 10.1214/25-ba1571
Authors: Hanyu Song, David Dunson
Institution: Duke University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7140729243